A fundamental component of music rhythm, time signatures display the meter of a piece or section of music.
A time signature is composed of a top number and a bottom number. A common confusion is that the top number is the number of beats, and the bottom number is the beat unit, but this is only the case for simple meter.
Time signatures are best explained by example. Let's take 3/4 for starters:
3/4 time (pronounced "three-four time" and also called 3/4 meter) means that there are a total of three quarter notes in each measure (also called bar).
In the case of a 4/4 time signature:
... each measure totals four quarter notes. The bottom number tells us that the unit is a quarter note, and the top tells us that there are a total of four of them in each measure.
The above examples are of simple meter. In 3/4 meter, there are indeed three beats per measure, and each beat is a quarter note.
In compound meter, on the other hand, this is not the case. Let's illustrate using 6/8:
Here, there are a total of six eighth notes per measure. There are only two beats, however, each of which totals a dotted quarter (which equals three eighth notes). To understand this concept, please read Compound Meter.
An important aspect of time signatures is that they organize notes visually into beats. In the above example of 6/8 meter, the eye can immediately see that the measure is cut in half, with two beams in the measure. This is to help the eye by organizing the musical information in a natural and logical manner.